Jeremy Corbyn said he was "not a huge fan" of the European Union but was 70-75% in favour of the UK staying in for the sake of workers' rights and the environment.
The Opposition leader defended his decision not to share platforms with David Cameron, insisting the Prime Minister was pursuing a "totally different argument".
His appeal to Labour voters during an appearance on Channel 4's The Last Leg comedy chat show came as one opinion poll showed the Leave campaign taking a 10-point lead.
The survey by ORB for The Independent put the scores at 55% to 45% in favour of pulling out of the European Union, after allowing for an individual's likelihood to vote.
That is a four-point jump in support from April when Vote Leave led by 51 to 49 and an exact reversal of the position when the series of surveys began a year ago.
A 56% majority of 2015 Labour voters - seen as pivotal to the result - back continued membership but 44% are pro-Brexit - while Tories are 62% to 38% in favour of divorce from Brussels
Mr Corbyn, who has a history of Euroscepticism, has been criticised for an apparently lukewarm commitment to the campaign for an in vote on June 23.
He said he was not surprised that prominent Labour backbencher John Mann had joined the pro-Brexit camp but insisted he was committed to pushing the rival case.
"I am not a huge fan of the European Union. What I believe is that this is a practical decision that we take in order to get better conditions across the whole continent for everybody," he said.
He downplayed the role of Brussels in securing rights such as paid holiday and maternity leave which he said "wasn't a gift from the European Union, it was collective action by unions across Europe".
But he said co-operation within the bloc was vital in a range of areas.
Asked to rate his passion for keeping the UK in the EU on a scale of one to 10, he said: "We're looking at seven, seven and a half".
Tories such as the PM wanted a Europe "dominated by global corporations" and would back the so-called TTIP trade deal with the US that Mr Corbyn opposes, he said.
"I want to see a Europe that is about social cohesion, that is about better human rights, that is about workers' rights and is also about taking a European response to help victims of wars who are going through the most appalling situation on the borders of Europe at the moment.
"I suspect his views are different".
It came after Labour stepped up its campaigning with a warning that a vote to leave the EU would usher in a "hard right" Tory government committed to a new wave of cuts.
Ed Miliband led a clutch of senior party figures in insisting Brexit was not the solution to widespread concerns over the impact of immigration.
Deputy leader Tom Watson published an analysis claiming the Conservatives would be forced to hike VAT and slash spending to cover a £28 billion "black hole" in the public finances.
Concerns about losing Labour voters to Leave were intensified with the announcement that two more prominent backbenchers - Mr Mann and Dennis Skinner - had joined the handful of Labour MPs in the Brexit camp.